Clothes follows path then flies away
This was done in Vers 2..77a.  As far as I can tell the physics and particles engines in 2.8+ are much the same so all should work as described.  I believe it's the interface that's been changed.  (Blend file is below)



Details -

A single note was added - a plane, with an array modifier to make it a stack of 6.  The modifier was applied so it's a stack of planes but now a single mesh'd object. 
Frankly I see this step as a waste of time unless an audience or player can actually see it's a single plane in lieu of.

The ATM's slot has a curve->path added and perpendicular to it so it curves up and out from the slot, something like a launch ramp.

The curve's ATM end is well back behind the slot so the notes won't show initially.   It's outside end is curved up so the notes will be angled at around 45 to 60 degrees.

A curve modifier is used and the note stack is animated along it's X axis.  The stack travels along and up the curve over about a half second.  (You could use a path constraint as an alternative)

The stack of notes, whilst a single object still consists of 6 planes so the whole thing was duplicated and de-animated, it's inherited physics also switched off so we have six faces from which to emit 6 notes as particles.  i.e. a particle emitter.
A single plane would do just as well, but emit from the face so the particles are launched from the center.

At the frame after the stack's curve-travel ceases, the emitter starts emitting the 6 notes over some 3 frames, and tweaked so they're traveling at much the same angle and direction as the stack.

The particles use a "Particle Object". (found in layer 9)  That's just a plane, textured to look like currency and shapekeyed over a few frames so it curls a bit after ejection.  (Cloth physics didn't want to work in this case)

Because particles are fond of penetrating surfaces they're supposed to bounce off, an invisible collision surface (an invisible plane) is placed above the visible shelf.  The shelf therefore normally wouldn't need physics.

The original note stack can be switched to invisible once the particles take over.

From there it's a matter of tweaking the emitter so the notes behave as required.  Some experimentation might be needed.